theory
New in version 1.0.3.
Module for theoretical calculations.
- nexus.theory.CoherenceTime(coherence_length)
Calculates the coherence time of a given longitudinal coherence length \(\xi_{\parallel}\)
\[\tau = \frac{\xi_{\parallel}}{c}.\]New in version 1.0.3.
- Parameters:
coherence_length (float) – longitudinal coherence length (m).
- Returns:
coherence time (s).
- Return type:
float
- nexus.theory.CrossSection(energy, isotope)
Calculates the absorption cross section [Gonser]
\[I = \sigma_0 \frac{\Gamma^2}{4(E-E_0)^2+\Gamma^2}\]New in version 1.0.3.
- Parameters:
energy (float or list or ndarray) – energy value(s) (eV).
isotope (
MoessbauerIsotope) – Isotope for the calculation.
- Returns:
absorption.
- Return type:
float or ndarray
- nexus.theory.DebyeTemperatureImpurity(Debye_temperature, mass_host, mass_impurity)
Calculates the Debye temperature for an impurity atom in a host matrix [Gonser]
\[\Theta^I_D = \sqrt{\frac{M_{host}}{M_{impurity}}}\Theta_D\]New in version 1.0.3.
- Parameters:
Debye_temperature (float) – Debye temperature of the host material (K).
mass_host (float) – mass of the host atom.
mass_impurity (float) – mass of the impurity atom.
- Returns:
Debye temperature of the impurity (K).
- Return type:
float
- nexus.theory.DopplerEnergy(value, velocity)
Calculates the Doppler shifted energy or frequency [Gonser]
\[E_{\gamma} = \left(1 + \frac{v}{c}\right) E_0\]- Parameters:
value (float) – energy or frequency in units of choice.
velocity (float) – velocity (m/s).
- Returns:
shifted energy or frequency.
- Return type:
float
- nexus.theory.DopplerShift(value, velocity)
Calculates the Doppler shift of energy or frequency [Gonser]
\[\Delta E = \frac{v}{c} E\]- Parameters:
value (float) – energy or frequency in units of choice.
velocity (float) – velocity (m/s).
- Returns:
Doppler shift of energy or frequency.
- Return type:
float
- nexus.theory.HalfLifetime(lifetime)
Calculates the half lifetime \(t_{\frac{1}{2}}\) [Gonser]
\[t_{\frac{1}{2}} = \ln(2) \tau\]- Parameters:
lifetime (float) – lifetime \(\tau\) (arb. units).
- Returns:
half lifetime (in units of lifetime).
- Return type:
float
- nexus.theory.LambMoessbauerDebye(temperature, Debye_temperature, energy, mass)
Calculates the Lamb Moessbauer factor in the Debye model [Gonser]
\[f_{LM} = \exp\left( -\frac{3 E_R}{2k_B\Theta_D} \left( 1+ 4 \left(\frac{T}{\Theta_D}\right)^2 \int_0^{\frac{\Theta_D}{T}} \frac{x}{e^x-1}dx \right) \right)\]New in version 1.0.3.
- Parameters:
temperature (float) – real temperature (K).
Debye_temperature (float) – Debye temperature (K).
energy (float) – Photon energy (eV).
mass (float) – mass in atomic mass units (amu).
- Returns:
Lamb Moessbauer factor.
- Return type:
float
- nexus.theory.LambMoessbauerDebyeIsotope(temperature, Debye_temperature, isotope)
Calculates the Lamb Moessbauer factor in the Debye model [Gonser]
\[f_{LM} = \exp\left( -\frac{3 E_R}{2k_B\Theta_D} \left( 1+ 4 \left(\frac{T}{\Theta_D}\right)^2 \int_0^{\frac{\Theta_D}{T}} \frac{x}{e^x-1}dx \right) \right)\]New in version 1.0.3.
- Parameters:
temperature (float) – real temperature (K).
Debye_temperature (float) – Debye temperature (K).
isotope (
MoessbauerIsotope) – isotope for the calculation.
- Returns:
Lamb Moessbauer factor.
- Return type:
float
- nexus.theory.LongitudinalCoherence(wavelength, bandwidth)
Calculates the longitudinal coherence length for a given wavelength and its bandwidth via
\[\xi_{\parallel} = \left(\frac{\lambda}{2}\right) \left(\frac{\lambda}{\Delta\lambda}\right)\]New in version 1.0.3.
- Parameters:
wavelength (float) – Photon wavelength \(\lambda\) (m).
bandwidth (float) – Photon wavelength bandwidth \(\Delta\lambda\) in (m).
- Returns:
longitudinal coherence length (m).
- Return type:
float
- nexus.theory.LongitudinalCoherenceEnergy(energy, bandwidth)
Calculates the longitudinal coherence length for a given energy and its bandwidth.
\[\xi_{\parallel} = \hbar c \frac{1 + \frac{\Delta E}{E}}{2 \Delta E}\]New in version 1.0.3.
- Parameters:
energy (float) – Photon energy (eV).
bandwidth (float) – Photon energy bandwidth \(\Delta E\) in (eV).
- Returns:
longitudinal coherence length (m).
- Return type:
float
- nexus.theory.LongitudinalCoherenceFromTime(coherence_time)
Calculates the longitudinal coherence length from a given coherence time \(\tau\)
\[\xi_{\parallel} = \tau c\]New in version 1.0.3.
- Parameters:
coherence_time (float) – coherence time (s).
- Returns:
longitudinal coherence length (m).
- Return type:
float
- nexus.theory.MagneticEnergy(m, g, Bhf)
Calculates the magnetic energy due to a hyperfine field [Gonser]
\[E = -mg \mu_N B_{hf}\]New in version 1.0.3.
- Parameters:
isotope (
MoessbauerIsotope) – Isotope for the calculation.Bhf (float) – Magnetic hyperfine field (T).
- Returns:
energy (eV).
- Return type:
float
- nexus.theory.MagneticEnergyDifference(mg, gg, me, ge, Bhf)
Calculates the magnetic energy difference of magnetically split lines [Gonser]
\[\Delta E =\left(m_e g_e - m_g g_g \right)\mu_N B_{hf}\]New in version 1.0.3.
- Parameters:
mg (float) – magnetic quantum number of the ground state.
gg (float) – g factor of the ground state.
me (float) – magnetic quantum number of the excited state.
ge (float) – g factor of the excited state.
Bhf (float) – Magnetic hyperfine field (T).
- Returns:
energy (eV).
- Return type:
float
- nexus.theory.MagneticSplittingSextet(isotope, Bhf)
Calculates the outer line splitting of a magnetic sextet, like for Fe57,
\[\Delta E = B_{hf} \mu_N \left(3|g_e| + |g_g| \right).\]New in version 1.0.3.
- Parameters:
isotope (
MoessbauerIsotope) – Isotope for the calculation.Bhf (float) – Magnetic hyperfine field (T)
- Returns:
energy (eV).
- Return type:
float
- nexus.theory.MagneticSplittingSextetVelocity(isotope, Bhf)
Calculates the outer line splitting velocity of a magnetic sextet, like for Fe57, in units of velocity
New in version 1.0.3.
- Parameters:
isotope (
MoessbauerIsotope) – Isotope for the calculation.Bhf (float) – Magnetic hyperfine field (T).
- Returns:
velocity spacing (mm/s).
- Return type:
float
- nexus.theory.NuclearMagneticMoment(g, I)
Calculates the nuclear magnetic moment [Gonser] and [Drago]
\[\mu = g \mu_N I\]New in version 1.0.3.
- Parameters:
g (float) – g-factor of the (ground or excited) state.
I (float) – Spin of the (ground or excited) state.
- Returns:
nuclear magnetic moment (eV/T).
- Return type:
float
- nexus.theory.QuadrupoleEnergy(I, m, Q, Vzz, asymmetry)
Calculates the quadrupole energy for I=3/2 [Gonser] and [Drago]
\[E = \frac{eQV_{zz}}{4I(2I+1)} \left(3m^2-I(I+1))\right) \sqrt{1 + \frac{\eta^2}{3}},\]New in version 1.0.3.
- Parameters:
I (float) – Spin of the (ground or excited) state \(I\).
m (float) – magnetic quantum number \(m = -I, ..., I\).
Q (float) – Quadrupole moment (barn).
Vzz (float) – Electric field gradient along main axis (V/m2).
asymmetry – Asymmetry parameter \(\eta\) (dimensionless 0 to 1).
- Returns:
Quadrupole energy (eV).
- Return type:
float
- nexus.theory.QuadrupoleSplittingDoublet(Q, Vzz, asymmetry)
Calculates the quadrupole splitting for a doublet (I = 3/2) [Gonser] and [Drago]
\[\Delta E = \frac{eQV_{zz}}{2} \sqrt{1 + \frac{\eta^2}{3}},\]New in version 1.0.3.
- Parameters:
Q (float) – Quadrupole moment (barn).
Vzz (float) – Electric field gradient along main axis (V/m2). Note, \(V_{zz} = eq_{zz}\), where \(q_{zz}\) is the direction of the z-axis of the field gradient.
asymmetry – Asymmetry parameter \(\eta\) (dimensionless 0 to 1).
- Returns:
Quadrupole energy (eV).
- Return type:
float
- nexus.theory.QuadrupoleSplittingDoubletVelocity(isotope, Q, Vzz, asymmetry)
Calculates the quadrupole splitting for a doublet (I = 3/2) in units of the velocity [Gonser] and [Drago]
New in version 1.0.3.
- Parameters:
isotope (
MoessbauerIsotope) – Isotope for the calculation.Q (float) – Quadrupole moment (barn).
Vzz (float) – Electric field gradient along main axis (V/m2). Note, \(V_{zz} = eq_{zz}\), where \(q_{zz}\) is the direction of the z-axis of the field gradient.
asymmetry – Asymmetry parameter \(\eta\) (dimensionless 0 to 1).
- Returns:
velocity spacing (mm/s).
- Return type:
float
- nexus.theory.RecoilEnergy(energy, mass)
Calculates the recoil energy of a photon at mass \(m\) [Gonser]
\[R = \frac{E^2}{2mc^2}\]- Parameters:
energy (float) – Photon energy (eV).
mass (float) – mass in atomic mass units (amu).
- Returns:
recoil energy (eV).
- Return type:
float
- nexus.theory.RecoilEnergyIsotope(isotope)
Calculates the recoil energy of a photon at a specific isotope [Gonser]
\[R = \frac{E^2}{2m_{I}c^2}\]New in version 1.0.3.
- Parameters:
energy (
MoessbuaerIsotope) – Isotope for the calculation.- Returns:
recoil energy (eV).
- Return type:
float
- nexus.theory.SecondOrderDopplerDebye(temperature, Debye_temperature, energy, mass)
Calculates the second order Doppler shift for a given temperature in the Debye model [Tanaka]
\[\Delta E = -E \frac{9 k_B \Theta_D}{16 M c^2} \left( 1 + 8 \left(\frac{T}{\Theta_D}\right)^4 \int_0^{\frac{\Theta_D}{T}} \frac{x^3}{e^x-1}dx \right)\]New in version 1.0.3.
- Parameters:
temperature (float) – real temperature (K).
Debye_temperature (float) – Debye temperature (K).
energy (float) – Transition energy (eV).
mass (float) – atomic mass in atomic units (amu).
- Returns:
Energy shift (eV).
- Return type:
float
- nexus.theory.SecondOrderDopplerDebyeIsotope(temperature, Debye_temperature, isotope)
Calculates the second order Doppler shift for a given temperature in the Debye model [Tanaka]
\[\Delta E = -E \frac{9 k_B \Theta_D}{16 M c^2} \left( 1 + 8 \left(\frac{T}{\Theta_D}\right)^4 \int_0^{\frac{\Theta_D}{T}} \frac{x^3}{e^x-1}dx \right)\]New in version 1.0.3.
- Parameters:
temperature (float) – real temperature (K).
Debye_temperature (float) – Debye temperature (K).
isotope (
MoessbauerIsotope) – isotope for the calculation.
- Returns:
Energy shift (eV).
- Return type:
float
- nexus.theory.SecondOrderDopplerDebyeVelocity(temperature, Debye_temperature, mass)
Calculates the second order Doppler shift in units of velocity for a given temperature in the Debye model.
\[SOD = -\frac{9 k_B \Theta_D}{16 M c} \left( 1 + 8 \left(\frac{T}{\Theta_D}\right)^4 \int_0^{\frac{\Theta_D}{T}} \frac{x^3}{e^x-1}dx \right)\]New in version 1.0.4.
- Parameters:
temperature (float) – real temperature (K).
Debye_temperature (float) – Debye temperature (K).
mass (float) – atomic mass in atomic units (amu).
- Returns:
SOD (mm/s).
- Return type:
float
- nexus.theory.SecondOrderDopplerDebyeVelocityIsotope(temperature, Debye_temperature, isotope)
Calculates the second order Doppler shift in units of velocity for a given temperature in the Debye model.
\[SOD = -\frac{9 k_B \Theta_D}{16 M c} \left( 1 + 8 \left(\frac{T}{\Theta_D}\right)^4 \int_0^{\frac{\Theta_D}{T}} \frac{x^3}{e^x-1}dx \right)\]New in version 1.0.4.
- Parameters:
temperature (float) – real temperature (K).
Debye_temperature (float) – Debye temperature (K).
isotope (
MoessbauerIsotope) – isotope for the calculation.
- Returns:
SOD (mm/s).
- Return type:
float
- nexus.theory.SecondOrderDopplerShift(velocity_mean, energy)
Calculates the second order Doppler shift for a given mean squared velocity [Josephson]
\[\Delta E = -E \frac{\langle v^2 \rangle}{2 c^2}.\]New in version 1.0.3.
- Parameters:
velocity_mean (float) – Mean squared velocity ((m/s) 2 ).
energy (float) – Energy of the transition (eV).
- Returns:
Change in energy due to second order Doppler shift (eV).
- Return type:
float
- nexus.theory.SecondOrderDopplerVelocityShift(velocity_mean)
Calculates the second order Doppler shift for a given mean squared velocity [Nasu]
\[\Delta v = -\frac{\langle v^2 \rangle }{2 c}.\]New in version 1.0.3.
- Parameters:
velocity_mean (float) – Mean squared velocity ((m/s) 2 ).
- Returns:
Change in velocity due to second order Doppler shift (mm/s).
- Return type:
float
- nexus.theory.TransverseCoherence(wavelength, source_size, source_distance)
Calculates the transverse coherence
\[\xi_{\perp} = \left(\frac{\lambda}{2}\right) \left(\frac{d}{s}\right)\]This equation should be used for vertical and horizontal directions independently.
New in version 1.0.3.
- Parameters:
wavelength (float) – wavelength \(\lambda\) (m).
source_size (float) – Source size \(s\) in (m).
source_distance (float) – Source distance \(d\) in (m).
- Returns:
transverse coherence length (m).
- Return type:
float
- nexus.theory.TransverseCoherenceEnergy(energy, source_size, source_distance)
Calculates the transverse coherence
\[\xi_{\perp} = \left(\frac{hc}{2E}\right) \left(\frac{d}{s}\right)\]This equation should be used for vertical and horizontal directions independently.
New in version 1.0.3.
- Parameters:
energy (float) – energy (eV).
source_size (float) – Source size \(s\) in (m).
source_distance (float) – Source distance \(d\) in (m).
- Returns:
transverse coherence length (m).
- Return type:
float
- nexus.theory.TransverseCoherenceNRS(energy, source_size, source_distance, detector_size, detector_distance, sample_size=None)
Calculates the transverse coherence via
\[\xi_{\perp} = \left(\frac{hc}{2 E}\right) \left(\frac{1}{\pi\sigma}\right) \textrm{ with } \sigma^2 = \left( \frac{\sigma_0}{S} \right)^2 + \left( \frac{\sigma_d}{D} \right)^2 + \left( \frac{\sigma_s}{D}+\frac{\sigma_s}{S} \right)^2 + \frac{1}{4k^2\sigma_s^2}\]Here, especially the detector size typically determines the transverse coherence. This equation should be used for vertical and horizontal directions independently.
New in version 1.0.3.
- Parameters:
energy (float) – Photon energy (eV).
source_size (float) – Source size (Gaussian \(\sigma_0\)) (m).
source_distance (float) – Source-sample distance \(S\) (m).
detector_size (float) – Detector size (Gaussian \(\sigma_d\)) (m).
detector_distance (float) – Detector-sample distance \(D\) (m).
sample_size (float) – Sample size (Gaussian \(\sigma_s\)) (m), illuminated part, optional.
- Returns:
transverse coherence length (m).
- Return type:
float